Finite Group Databasebeta

← Prev (#32914846) Next (#32914848) →

C₉×D₁₀₂₇ #32914847

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₀₂₇

Splittings

Fitting, Hall	C₉×C₁₃×C₇₉ ⋊ C₂
derived, Hall	C₁₃×C₇₉ ⋊ C₂×C₉
Hall	C₉×C₇₉ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₇₉
Sylow	C₇₉ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₂₇
commutator, hypocenter	C₁₃×C₇₉	C₂×C₉
Frattini	C₃	C₃×D₁₀₂₇
Fitting	C₉×C₁₃×C₇₉	C₂
socle, cosocle	C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₃×D₁₀₂₇	C₃
LCS	G ▷ C₁₃×C₇₉
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9243

Conjugacy classes & character table

4635 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×D₇₉, D₉×D₁₀₂₇, D₁₁₇⋊D₇₉, …
maximal normal subgroup of	C₉×D₁₃×D₇₉, D₉×D₁₀₂₇, D₁₁₇⋊D₇₉, …
maximal quotient of	C₉×Dic₁₀₂₇, C₂×C₉×D₁₀₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 10);